A special board meeting is to be held on Monday, at 7pm in Kiwi Hall, to put a vote of no confidence in Mrs Carter on the table.
The requisition letter was made available on the council website yesterday.
Ms Robertson told the Times-Age yesterday that Mrs Carter "absolutely should know where it has come from".
She said although she did not have to list the reasons for calling the meeting, one of the main issues with Mrs Carter had been her way of communicating.
She said anyone elected to a board needed to be careful about making personal statements to media that may not reflect the position of the board.
Ms Robertson said issues within the board dated back to 2014 when "small problems were beginning to arise" and in the past six months there had been a definite split in the board.
Mrs Carter had called a board meeting in last September, with the subject being "unrest in the community board and solutions moving forward".
"Right back in September last year she knew she had problems within her board," Ms Robertson said.
"The unrest does illustrate she has been aware of the problems herself for a while."
Ms Robertson said she had a meeting with Mrs Carter on 6 February.
"[The meeting was] to express concerns that I had with the board and lack of confidence I had in her ability to lead the board."
Ms Robertson said having voted Mrs Carter into the position, this was not a path she had wanted to take.
"I nominated her for the role and had every confidence that she would do a good job."
However, "half the board no longer has the confidence in her ability".
At the meeting Ms Robertson had told Mrs Carter to step down.
"I knew we had the numbers to get a meeting on the table and she had the option to step down without it going public," Ms Robertson said.
"It was put to her that she could step down and she went away to think about it and came back and said 'no' she wouldn't, and that's why we are now in this unfortunate place where we are having to call a meeting."
With Mrs Carter stepping down from the role, it would allow the board to regroup, Ms Robertson said, adding Mrs Carter would still be a valid member of the board.
"I'm just really hoping that council get this matter resolved and the board can move on in a positive manner."